Block #587,406

TWNLength 11★★★☆☆

Bi-Twin Chain · Discovered 6/13/2014, 7:27:21 PM · Difficulty 10.9513 · 6,208,636 confirmations

TWN

Bi-Twin Chain

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

Block Header

Block Hash

2fd3b54fbaa99395ecbd6722aed027c7c37c7de3c4df93804ed370740cbf3d28

View on Chainz ↗

Height

#587,406

Difficulty

10.951343

Transactions

Size

887 B

Version

Bits

0af38b31

Nonce

124,888,001

Timestamp

6/13/2014, 7:27:21 PM

Confirmations

6,208,636

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

1b94cf9d947495df73cda113f222fe75b5eff120e4cec95b57e88d9d36cfc4b6

Transactions (4)

Coinbase1cde521e9c5a63…98116eb292a537

1 in → 1 out8.3500 XPM116 B

ANSXnLY2…Sd25TjkD

22719ce41b8465…e191b61545cebc

1 in → 2 out0.4924 XPM225 B

AcanX2TP…ckWhYAoG AexMzHff…BHwkPRGp

d2920b488369d5…1ea86d68143a7e

1 in → 2 out5.3944 XPM227 B

AGdWVjRk…LFVsqCnK Ac1eiomB…Fj7o6Yg3

4120bea7aa26e7…fea1a5fa69fd85

1 in → 2 out3.0999 XPM227 B

APC7foz1…9KM6jX3A AekdwfxU…kbhJFGTn

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.

1.375 × 10⁹⁹(100-digit number)

13758428299229982756…75492186030963312639

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

1.375 × 10⁹⁹(100-digit number)

13758428299229982756…75492186030963312639

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

1.375 × 10⁹⁹(100-digit number)

13758428299229982756…75492186030963312641

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

2.751 × 10⁹⁹(100-digit number)

27516856598459965513…50984372061926625279

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

2.751 × 10⁹⁹(100-digit number)

27516856598459965513…50984372061926625281

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

5.503 × 10⁹⁹(100-digit number)

55033713196919931027…01968744123853250559

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

5.503 × 10⁹⁹(100-digit number)

55033713196919931027…01968744123853250561

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

1.100 × 10¹⁰⁰(101-digit number)

11006742639383986205…03937488247706501119

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

1.100 × 10¹⁰⁰(101-digit number)

11006742639383986205…03937488247706501121

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

2.201 × 10¹⁰⁰(101-digit number)

22013485278767972411…07874976495413002239

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

2.201 × 10¹⁰⁰(101-digit number)

22013485278767972411…07874976495413002241

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

4.402 × 10¹⁰⁰(101-digit number)

44026970557535944822…15749952990826004479

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