Block #307,560

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 12/12/2013, 4:02:13 PM · Difficulty 9.9942 · 6,500,279 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

b2eeb153d0143d8508ae067a4b23d65dc143d6a1427bd998d4a2bf883ba0258a

View on Chainz ↗

Height

#307,560

Difficulty

9.994206

Transactions

Size

1.08 KB

Version

Bits

09fe8441

Nonce

66,746

Timestamp

12/12/2013, 4:02:13 PM

Confirmations

6,500,279

Mined by

⛏️ P2SHARJW3qkGSmeWmJAYGpFm1tTkU9edGsXmSR

Merkle Root

181913486b94bbb73e1553267b1c0d35d48eda49be66524eca5be71c66dbaf1b

Transactions (5)

Coinbase72397df78a259e…d09cfb5a8ad8f3

1 in → 1 out10.0400 XPM109 B

ARJW3qkG…edGsXmSR

88375cb09bc506…d2e8a09f74433a

1 in → 2 out4.8603 XPM227 B

AKHCvcEi…p59ZuSHb AUfZs9KH…a4h5GYWM

28b95559b55e8a…452ba27c3cbe5f

1 in → 2 out3.5008 XPM226 B

AUAN8oHh…ngAoCDLQ AH4PYrGR…zrqJu6kn

a35e3c858dcd65…4b9df055f7bb85

1 in → 2 out2.6626 XPM226 B

AG7ws3xY…bA6grwP7 AKdEYWP2…aYY5SXUq

eef8feb5eab36e…7c9aebc4a84026

1 in → 2 out1.9607 XPM227 B

AJ1dPkbQ…GxYnPcq9 Ad6bt69S…PfMPqrnD

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.

6.435 × 10⁹⁷(98-digit number)

64356494409184206628…98835499552899025919

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

6.435 × 10⁹⁷(98-digit number)

64356494409184206628…98835499552899025919

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

6.435 × 10⁹⁷(98-digit number)

64356494409184206628…98835499552899025921

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

1.287 × 10⁹⁸(99-digit number)

12871298881836841325…97670999105798051839

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.287 × 10⁹⁸(99-digit number)

12871298881836841325…97670999105798051841

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

2.574 × 10⁹⁸(99-digit number)

25742597763673682651…95341998211596103679

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.574 × 10⁹⁸(99-digit number)

25742597763673682651…95341998211596103681

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

5.148 × 10⁹⁸(99-digit number)

51485195527347365303…90683996423192207359

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

5.148 × 10⁹⁸(99-digit number)

51485195527347365303…90683996423192207361

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

1.029 × 10⁹⁹(100-digit number)

10297039105469473060…81367992846384414719

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

Block #307,560

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