Block #89,157

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 7/30/2013, 4:08:26 AM · Difficulty 9.2601 · 6,705,030 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

f56bf5ae0e7c6a0be70aa64a788194e1d0e9d5162c4612b9ac3c779417f5b266

View on Chainz ↗

Height

#89,157

Difficulty

9.260068

Transactions

Size

204 B

Version

Bits

094293d4

Nonce

46,184

Timestamp

7/30/2013, 4:08:26 AM

Confirmations

6,705,030

Merkle Root

87cfabf9d829dce388c850a5ccb22dd34d06245d0110254649a16d37671cdc80

Transactions (1)

Coinbase87cfabf9d829dc…a16d37671cdc80

1 in → 1 out11.6500 XPM109 B

AdhmaJ1p…MhFRDjQ7

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.

2.632 × 10¹⁰⁷(108-digit number)

26328436440947205131…77902903143685417599

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

2.632 × 10¹⁰⁷(108-digit number)

26328436440947205131…77902903143685417599

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.632 × 10¹⁰⁷(108-digit number)

26328436440947205131…77902903143685417601

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

5.265 × 10¹⁰⁷(108-digit number)

52656872881894410263…55805806287370835199

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.265 × 10¹⁰⁷(108-digit number)

52656872881894410263…55805806287370835201

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

1.053 × 10¹⁰⁸(109-digit number)

10531374576378882052…11611612574741670399

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.053 × 10¹⁰⁸(109-digit number)

10531374576378882052…11611612574741670401

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

2.106 × 10¹⁰⁸(109-digit number)

21062749152757764105…23223225149483340799

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.106 × 10¹⁰⁸(109-digit number)

21062749152757764105…23223225149483340801

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

4.212 × 10¹⁰⁸(109-digit number)

42125498305515528210…46446450298966681599

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