Block #840,710

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 12/5/2014, 8:28:12 AM · Difficulty 10.9743 · 5,969,922 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

8d2bef59b2025ce16d03cc8271560b3566e7b750f511d6fd6a589900bc693b4a

View on Chainz ↗

Height

#840,710

Difficulty

10.974266

Transactions

Size

651 B

Version

Bits

0af96981

Nonce

916,509,782

Timestamp

12/5/2014, 8:28:12 AM

Confirmations

5,969,922

Mined by

⛏️ P2SHANwVDff75uDAd4qzm4PmPkXJRHTo8aYrpw

Merkle Root

c3ef6945e380aa3debb4693d3f6b81d36c3150d748a63280de6a25566423e886

Transactions (3)

Coinbaseb728a46bacbefb…77bbce0e0fe24b

1 in → 1 out8.3100 XPM109 B

ANwVDff7…To8aYrpw

7587a69ba0f755…ff97690c3e057c

1 in → 2 out5.4133 XPM227 B

AUuFks9B…Mku5uPg7 AHRoBSh4…BSVTQ36Q

66df3291429408…632b79de72b3ca

1 in → 2 out2.1918 XPM225 B

AWeFTqSF…usRDA3NM Ae9pNo1t…as3uX46w

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.

9.951 × 10⁹⁴(95-digit number)

99515981451808161944…11849687094662285599

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

9.951 × 10⁹⁴(95-digit number)

99515981451808161944…11849687094662285599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.951 × 10⁹⁴(95-digit number)

99515981451808161944…11849687094662285601

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

1.990 × 10⁹⁵(96-digit number)

19903196290361632388…23699374189324571199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.990 × 10⁹⁵(96-digit number)

19903196290361632388…23699374189324571201

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

3.980 × 10⁹⁵(96-digit number)

39806392580723264777…47398748378649142399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.980 × 10⁹⁵(96-digit number)

39806392580723264777…47398748378649142401

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

7.961 × 10⁹⁵(96-digit number)

79612785161446529555…94797496757298284799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.961 × 10⁹⁵(96-digit number)

79612785161446529555…94797496757298284801

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

1.592 × 10⁹⁶(97-digit number)

15922557032289305911…89594993514596569599

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.592 × 10⁹⁶(97-digit number)

15922557032289305911…89594993514596569601

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

3.184 × 10⁹⁶(97-digit number)

31845114064578611822…79189987029193139199

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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

Block #840,710

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