Block #197,496

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 10/7/2013, 3:27:32 AM · Difficulty 9.8840 · 6,612,891 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

97dd6bbbed5ba17c7bf165a00623a0672bdad9c82afc733340a5fb492b5cdbe8

View on Chainz ↗

Height

#197,496

Difficulty

9.883985

Transactions

Size

7.97 KB

Version

Bits

09e24cd4

Nonce

11,398

Timestamp

10/7/2013, 3:27:32 AM

Confirmations

6,612,891

Mined by

⛏️ P2SHAeKEn3Gfftvu7YB9q7vLB4doHnS6Bhxr4i

Merkle Root

6410a788335f8e095e9bf5e36da881acfbc65b0a9eea745b89c9025b9945cc07

Transactions (3)

Coinbasee00f52efbd833b…4d082266b74ff0

1 in → 1 out10.3100 XPM109 B

AeKEn3Gf…S6Bhxr4i

3567e59eaaef85…e19499740fdc80

52 in → 1 out60.7208 XPM7.56 KB

Acd1BgN5…bE5c9NoN

e028b2f01d4c6e…ccea70cec3e71b

1 in → 2 out399.9900 XPM226 B

AG6o3ctv…GbFwoCpQ AeJWpQpG…VmUesv5b

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.

9.061 × 10⁹²(93-digit number)

90613119425266206770…40922144887641518079

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

9.061 × 10⁹²(93-digit number)

90613119425266206770…40922144887641518079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

9.061 × 10⁹²(93-digit number)

90613119425266206770…40922144887641518081

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

1.812 × 10⁹³(94-digit number)

18122623885053241354…81844289775283036159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.812 × 10⁹³(94-digit number)

18122623885053241354…81844289775283036161

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

3.624 × 10⁹³(94-digit number)

36245247770106482708…63688579550566072319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

3.624 × 10⁹³(94-digit number)

36245247770106482708…63688579550566072321

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

7.249 × 10⁹³(94-digit number)

72490495540212965416…27377159101132144639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

7.249 × 10⁹³(94-digit number)

72490495540212965416…27377159101132144641

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

1.449 × 10⁹⁴(95-digit number)

14498099108042593083…54754318202264289279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

1.449 × 10⁹⁴(95-digit number)

14498099108042593083…54754318202264289281

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 #197,496

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