Block #207,370

TWNLength 9★☆☆☆☆

Bi-Twin Chain · Discovered 10/13/2013, 9:59:07 AM · Difficulty 9.9025 · 6,596,825 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

38c11455fd7c73847f2810ae54c223f31868962a9e98f2d0601ae70b91e5817c

View on Chainz ↗

Height

#207,370

Difficulty

9.902483

Transactions

Size

5.00 KB

Version

Bits

09e7091e

Nonce

1,164,741,018

Timestamp

10/13/2013, 9:59:07 AM

Confirmations

6,596,825

Mined by

⛏️ *RZnAMbqCTSieCHyY4der1Zhf2taVGbgsSN2t2

Merkle Root

9519897831e900c40876cfd4428e911bd2e3eae328bf409fed6f6841121d77df

Transactions (4)

Coinbasecc76bda8c9cd68…cabebcdb357752

1 in → 113 out10.1400 XPM3.81 KB

AMbqCTSi…bgsSN2t2 ATQbkhZz…tNgntZJa AQvGmFRt…xEKL8LoR AZ5CSLLL…HvSdnGLG AaWqCG7N…dKcG2SFS

267bb8e728628e…37b9e140b88ae5

1 in → 2 out10.1800 XPM226 B

AJi6LL28…QQBF3qpM AHyHEeYQ…XuELsExj

be2a5adad18e45…98337ef50a9331

2 in → 2 out16.1795 XPM375 B

ASuoUi24…FwBoFbxd AecG9enR…sT7RPpQS

8fc13061a6259a…0052fa25ab9b32

3 in → 2 out5.0113 XPM521 B

AQJHwvA5…81T4aSj1 AGR7ZzvG…MzvJPKrB

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.

8.778 × 10⁹⁴(95-digit number)

87783225004001417602…60896955729770367999

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

8.778 × 10⁹⁴(95-digit number)

87783225004001417602…60896955729770367999

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

8.778 × 10⁹⁴(95-digit number)

87783225004001417602…60896955729770368001

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

1.755 × 10⁹⁵(96-digit number)

17556645000800283520…21793911459540735999

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.755 × 10⁹⁵(96-digit number)

17556645000800283520…21793911459540736001

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

3.511 × 10⁹⁵(96-digit number)

35113290001600567041…43587822919081471999

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.511 × 10⁹⁵(96-digit number)

35113290001600567041…43587822919081472001

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

7.022 × 10⁹⁵(96-digit number)

70226580003201134082…87175645838162943999

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.022 × 10⁹⁵(96-digit number)

70226580003201134082…87175645838162944001

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

1.404 × 10⁹⁶(97-digit number)

14045316000640226816…74351291676325887999

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