Block #2,585,397

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 3/25/2018, 7:21:59 PM · Difficulty 11.2517 · 4,252,680 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0ec4ce1c0654c6c01cee206466c37110221cc8502c16751a0c609872dd81c0bc

View on Chainz ↗

Height

#2,585,397

Difficulty

11.251653

Transactions

Size

1.81 KB

Version

Bits

0b406c5a

Nonce

626,763,370

Timestamp

3/25/2018, 7:21:59 PM

Confirmations

4,252,680

Mined by

⛏️ P2SHAdqah8zh3AxeLUnA13CQCRpLQc1WwoHJ9t

Merkle Root

558b2dd90047c3ff4f413769ec910d0bd36bbd02aa183f06997760e127c6ce30

Transactions (5)

Coinbase0f1b5a860ff963…b1ac41b11bb2c7

1 in → 1 out7.9300 XPM109 B

Adqah8zh…1WwoHJ9t

8bea7994e7b05f…a2b5a0cba6ca4a

2 in → 2 out16.1700 XPM304 B

ALKFdkt9…bkfhxLnz ALmkefdM…V1vaLtJW

06550de589851d…14e2a2c53cf6e8

2 in → 2 out16.1500 XPM307 B

AW3QZZmg…j2rGjUkp AHmC4haH…brfxcDWL

972544639f4171…1a25b250385348

4 in → 2 out10.1600 XPM671 B

AVManj7t…z45RvHGu AbSGGh4x…fuPE5NVc

3ed9b6f7ec5014…0f65b039fc3ab5

2 in → 2 out12.3100 XPM376 B

AduVdu5q…3LY8rRGc AWFeaKY3…RDKGoMkf

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.

2.553 × 10⁹⁶(97-digit number)

25534217473891234732…01044792181873704959

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

2.553 × 10⁹⁶(97-digit number)

25534217473891234732…01044792181873704959

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

2.553 × 10⁹⁶(97-digit number)

25534217473891234732…01044792181873704961

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

5.106 × 10⁹⁶(97-digit number)

51068434947782469465…02089584363747409919

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

5.106 × 10⁹⁶(97-digit number)

51068434947782469465…02089584363747409921

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

1.021 × 10⁹⁷(98-digit number)

10213686989556493893…04179168727494819839

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.021 × 10⁹⁷(98-digit number)

10213686989556493893…04179168727494819841

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

2.042 × 10⁹⁷(98-digit number)

20427373979112987786…08358337454989639679

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

2.042 × 10⁹⁷(98-digit number)

20427373979112987786…08358337454989639681

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

4.085 × 10⁹⁷(98-digit number)

40854747958225975572…16716674909979279359

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

4.085 × 10⁹⁷(98-digit number)

40854747958225975572…16716674909979279361

Verify on FactorDB ↗Wolfram Alpha ↗

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

Level 5 — Twin Prime Pair (2^5 × origin ± 1)

2^5 × origin − 1

8.170 × 10⁹⁷(98-digit number)

81709495916451951145…33433349819958558719

Verify on FactorDB ↗Wolfram Alpha ↗

What this block proved

The miner who found this block proved the existence of 11 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

RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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 #2,585,397

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