Block #345,807

TWNLength 13★★★★★

Bi-Twin Chain · Discovered 1/6/2014, 4:19:00 AM · Difficulty 10.2140 · 6,445,505 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

ad0bdbfa2b879d0d8a439a65c693d70fa4ece9f26b22b7862e99700f363cc3a9

View on Chainz ↗

Height

#345,807

Difficulty

10.213965

Transactions

Size

1.08 KB

Version

Bits

0a36c66f

Nonce

153,624

Timestamp

1/6/2014, 4:19:00 AM

Confirmations

6,445,505

Merkle Root

4e150019f48f39655fda8810059b07238775a6d1115a6496635459536badabed

Transactions (5)

Coinbase52efaa629b7702…416f14035fc805

1 in → 1 out9.6100 XPM110 B

AeKNrjNj…1NEq95Ta

edaf2fbe3ea61c…f7b70e27ef9b74

1 in → 2 out4.6252 XPM226 B

AUcuMnfn…BzsFqrnH AdPxK7Xb…oRhhbocC

67efd424fb8b20…673408088ce392

1 in → 2 out4.5036 XPM226 B

APYH8xDg…5P6m2FkS AGxMeQpn…PtE4vAxN

aa70a6248dffdb…b8439a8e24ae3d

1 in → 2 out2.1414 XPM226 B

AeW1rttf…s9QpwuSL AcBLEghw…h5w9ubuG

c99c9f284718cf…996b3745a2a950

1 in → 2 out1.4094 XPM226 B

AUFumkos…3NYtV8dZ AdQDvJer…nhRSdoEz

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

3.866 × 10⁹⁰(91-digit number)

38669569780296769766…91516912081601772879

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

3.866 × 10⁹⁰(91-digit number)

38669569780296769766…91516912081601772879

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.866 × 10⁹⁰(91-digit number)

38669569780296769766…91516912081601772881

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

7.733 × 10⁹⁰(91-digit number)

77339139560593539533…83033824163203545759

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.733 × 10⁹⁰(91-digit number)

77339139560593539533…83033824163203545761

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

1.546 × 10⁹¹(92-digit number)

15467827912118707906…66067648326407091519

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.546 × 10⁹¹(92-digit number)

15467827912118707906…66067648326407091521

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

3.093 × 10⁹¹(92-digit number)

30935655824237415813…32135296652814183039

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.093 × 10⁹¹(92-digit number)

30935655824237415813…32135296652814183041

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

6.187 × 10⁹¹(92-digit number)

61871311648474831626…64270593305628366079

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.187 × 10⁹¹(92-digit number)

61871311648474831626…64270593305628366081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

1.237 × 10⁹²(93-digit number)

12374262329694966325…28541186611256732159

Verify on FactorDB ↗Wolfram Alpha ↗

2^5 × origin + 1

1.237 × 10⁹²(93-digit number)

12374262329694966325…28541186611256732161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^5 × origin + 1 − 2^5 × origin − 1 = 2 (twin primes ✓)

Level 6 — Twin Prime Pair (2^6 × origin ± 1)

2^6 × origin − 1

2.474 × 10⁹²(93-digit number)

24748524659389932650…57082373222513464319

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 13 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★★★★

Rarity

LegendaryChain length 13

Roughly 1 in 100,000 blocks. Extremely rare — celebrated by the community.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer