Block #351,347

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 1/9/2014, 3:40:35 PM · Difficulty 10.2949 · 6,473,303 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2c6a88e31cf11f6b496488afe659065b52d05d731120d7ba3c914850b82b3dd0

View on Chainz ↗

Height

#351,347

Difficulty

10.294880

Transactions

Size

834 B

Version

Bits

0a4b7d40

Nonce

143,174

Timestamp

1/9/2014, 3:40:35 PM

Confirmations

6,473,303

Mined by

⛏️ s\AMQC4aya4xubziAP8jJGG5nLpZc4ptxi3K

Merkle Root

84b6f9a64ca4b4540d383c79390ca687c474927a9db8088ac6cd2980057442f0

Transactions (2)

Coinbaseb1c2914046d62b…874fb601d2929c

1 in → 10 out9.4300 XPM403 B

AMQC4aya…c4ptxi3K AN9emqpK…WEnrfX7s Acs9SHrk…QJSB8SFG AQFhQpUS…HmKbSyAx AHsam4Jq…SaRxY92h

f23627d1294fa2…9fcc2dd1334c87

2 in → 1 out5.5663 XPM340 B

AeZ2Rybj…27kvSxyM

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.

1.354 × 10⁹⁸(99-digit number)

13542568138030027263…75257436307099989759

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

1.354 × 10⁹⁸(99-digit number)

13542568138030027263…75257436307099989759

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.354 × 10⁹⁸(99-digit number)

13542568138030027263…75257436307099989761

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

2.708 × 10⁹⁸(99-digit number)

27085136276060054526…50514872614199979519

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.708 × 10⁹⁸(99-digit number)

27085136276060054526…50514872614199979521

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

5.417 × 10⁹⁸(99-digit number)

54170272552120109052…01029745228399959039

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.417 × 10⁹⁸(99-digit number)

54170272552120109052…01029745228399959041

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

1.083 × 10⁹⁹(100-digit number)

10834054510424021810…02059490456799918079

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.083 × 10⁹⁹(100-digit number)

10834054510424021810…02059490456799918081

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

2.166 × 10⁹⁹(100-digit number)

21668109020848043620…04118980913599836159

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.166 × 10⁹⁹(100-digit number)

21668109020848043620…04118980913599836161

Verify on FactorDB ↗Wolfram Alpha ↗

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

What this block proved

The miner who found this block proved the existence of 10 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

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

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 #351,347

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