Block #601,304

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/25/2014, 10:37:16 AM · Difficulty 10.9151 · 6,208,113 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

0084b1fc583f3a80a957a6bf930d51c4c6530da85f1db8417ffbd401cc44d0b8

View on Chainz ↗

Height

#601,304

Difficulty

10.915062

Transactions

Size

660 B

Version

Bits

0aea4188

Nonce

2,107,689,263

Timestamp

6/25/2014, 10:37:16 AM

Confirmations

6,208,113

Mined by

⛏️ gLANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

e93f87d3fd75d6120a4eb9e650ead3c49a50dbd6792e07de35b9ccb7e6b739fd

Transactions (3)

Coinbase22f8e1ff41e645…88634101f6182c

1 in → 1 out8.4000 XPM116 B

ANSXnLY2…Sd25TjkD

bfe4ed69261566…2471aacb939f0d

1 in → 2 out1.5833 XPM226 B

AWAwVNg1…ezF8WmBs ANCDHDVb…w8vj4cEd

c600cf2d680e66…08dc45db7efbdd

1 in → 2 out1.9855 XPM227 B

AVx1LcLU…qQ7gJNv9 AToctXWm…mgEtBv9N

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.

3.823 × 10⁹⁷(98-digit number)

38237098970799197985…54768286561746557899

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

3.823 × 10⁹⁷(98-digit number)

38237098970799197985…54768286561746557899

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

3.823 × 10⁹⁷(98-digit number)

38237098970799197985…54768286561746557901

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

7.647 × 10⁹⁷(98-digit number)

76474197941598395970…09536573123493115799

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

7.647 × 10⁹⁷(98-digit number)

76474197941598395970…09536573123493115801

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

1.529 × 10⁹⁸(99-digit number)

15294839588319679194…19073146246986231599

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

1.529 × 10⁹⁸(99-digit number)

15294839588319679194…19073146246986231601

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

3.058 × 10⁹⁸(99-digit number)

30589679176639358388…38146292493972463199

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

3.058 × 10⁹⁸(99-digit number)

30589679176639358388…38146292493972463201

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

6.117 × 10⁹⁸(99-digit number)

61179358353278716776…76292584987944926399

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

6.117 × 10⁹⁸(99-digit number)

61179358353278716776…76292584987944926401

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

1.223 × 10⁹⁹(100-digit number)

12235871670655743355…52585169975889852799

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 #601,304

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