Block #88,903

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/29/2013, 11:25:31 PM · Difficulty 9.2646 · 6,721,172 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

d6d7b49587794e5ff5c7a0364f578ad9273dfffbc5683b0c6aa2bb5c280a6e49

View on Chainz ↗

Height

#88,903

Difficulty

9.264607

Transactions

Size

5.04 KB

Version

Bits

0943bd42

Nonce

198,450

Timestamp

7/29/2013, 11:25:31 PM

Confirmations

6,721,172

Mined by

⛏️ P2SHAWTVDp3WVGQJUCejCKbQGDxroLjWyVvijV

Merkle Root

a0f48db659df913656e9a181f9a76eeb744e22a474137cd87b858319513f8a94

Transactions (4)

Coinbase41ac24e4f40d84…7a6a6b99ba8eee

1 in → 1 out11.7100 XPM109 B

AWTVDp3W…jWyVvijV

178298babd2169…05276893dcd372

35 in → 2 out3011.2400 XPM4.03 KB

ANzsN34E…3LhEDyXA AZiCNyEn…BjhGoBch

74b8bfc35f1992…acdd6dde1aaa51

1 in → 1 out11.5800 XPM158 B

AeTde7fH…w7crTzqr

2918b036cc9859…967b4ad26ce65c

4 in → 2 out8.0004 XPM669 B

AdZYYGvM…oZqoHg26 AX1GdVwS…meHTZbpa

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.

1.483 × 10¹⁰⁵(106-digit number)

14839721554081882150…02502636495484006179

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

1.483 × 10¹⁰⁵(106-digit number)

14839721554081882150…02502636495484006179

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.483 × 10¹⁰⁵(106-digit number)

14839721554081882150…02502636495484006181

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

2.967 × 10¹⁰⁵(106-digit number)

29679443108163764301…05005272990968012359

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.967 × 10¹⁰⁵(106-digit number)

29679443108163764301…05005272990968012361

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

5.935 × 10¹⁰⁵(106-digit number)

59358886216327528603…10010545981936024719

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.935 × 10¹⁰⁵(106-digit number)

59358886216327528603…10010545981936024721

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

1.187 × 10¹⁰⁶(107-digit number)

11871777243265505720…20021091963872049439

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.187 × 10¹⁰⁶(107-digit number)

11871777243265505720…20021091963872049441

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

2.374 × 10¹⁰⁶(107-digit number)

23743554486531011441…40042183927744098879

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 #88,903

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