Block #125,391

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 8/20/2013, 5:23:09 AM · Difficulty 9.7769 · 6,670,243 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d9e07bfcadc17d7861a4e6a43979e7b67e1cae591330fe651aefd26b7679c821

View on Chainz ↗

Height

#125,391

Difficulty

9.776912

Transactions

Size

889 B

Version

Bits

09c6e3bc

Nonce

45,993

Timestamp

8/20/2013, 5:23:09 AM

Confirmations

6,670,243

Mined by

⛏️ P2SHAYyPPXgF5A3RKbdbyWYgDSxAkdb6nr5cD2

Merkle Root

c61114c20f28ae261e4aad045d409b7d287454b014a30e7401023018b2ca906e

Transactions (4)

Coinbase9ed34e365b1603…5cbf44f611eb71

1 in → 1 out10.4800 XPM109 B

AYyPPXgF…b6nr5cD2

eabcbf868d918d…bc93ee13dc32d1

2 in → 1 out20.9900 XPM271 B

AFtap2en…4d4n6Nrg

856b3587aef782…d382faadf1c092

1 in → 2 out10.4900 XPM192 B

AGZvBxxa…shhkwtTn ATmrN1KJ…FSmbgUaw

7414a639f2334d…d731bfe831bb18

1 in → 2 out10.4800 XPM227 B

AW4CP3w1…iLy8Eh6g APT1gnFE…LUuGjPss

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.

2.815 × 10⁹⁴(95-digit number)

28155118637558004553…04898370874256564049

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

2.815 × 10⁹⁴(95-digit number)

28155118637558004553…04898370874256564049

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.815 × 10⁹⁴(95-digit number)

28155118637558004553…04898370874256564051

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

5.631 × 10⁹⁴(95-digit number)

56310237275116009106…09796741748513128099

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.631 × 10⁹⁴(95-digit number)

56310237275116009106…09796741748513128101

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

1.126 × 10⁹⁵(96-digit number)

11262047455023201821…19593483497026256199

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.126 × 10⁹⁵(96-digit number)

11262047455023201821…19593483497026256201

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

2.252 × 10⁹⁵(96-digit number)

22524094910046403642…39186966994052512399

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.252 × 10⁹⁵(96-digit number)

22524094910046403642…39186966994052512401

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

4.504 × 10⁹⁵(96-digit number)

45048189820092807285…78373933988105024799

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 9 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

CommonChain length 9

Found in most blocks. The baseline for Primecoin's proof-of-work.

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