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Block #589,562

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/15/2014, 1:57:09 PM Β· Difficulty 10.9474 Β· 6,234,997 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
4495df3a6badefb93f03f271931ef0bc60971b856b4ad81750f1f51fce73beb1
View on Chainz β†—

Height

#589,562

Difficulty

10.947448

Transactions

1

Size

207 B

Version

2

Bits

0af28bec

Nonce

105,946,915

Timestamp

6/15/2014, 1:57:09 PM

Confirmations

6,234,997

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

3becb9c50503bc73770c93218769e3af2bc339e4a83a935fab88a567b59568b1
Transactions (1)
Coinbase3becb9c50503bc…88a567b59568b1
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) β€” it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

1.034 Γ— 10⁹⁸(99-digit number)
10342616489542793483…59858427576978731839
Discovered Prime Numbers
Lower: 2^k Γ— origin βˆ’ 1 | Upper: 2^k Γ— 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 β€” Twin Prime Pair (origin Β± 1)
origin βˆ’ 1
1.034 Γ— 10⁹⁸(99-digit number)
10342616489542793483…59858427576978731839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.034 Γ— 10⁹⁸(99-digit number)
10342616489542793483…59858427576978731841
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: origin + 1 βˆ’ origin βˆ’ 1 = 2 (twin primes βœ“)
Level 1 β€” Twin Prime Pair (2^1 Γ— origin Β± 1)
2^1 Γ— origin βˆ’ 1
2.068 Γ— 10⁹⁸(99-digit number)
20685232979085586966…19716855153957463679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.068 Γ— 10⁹⁸(99-digit number)
20685232979085586966…19716855153957463681
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^1 Γ— origin + 1 βˆ’ 2^1 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 2 β€” Twin Prime Pair (2^2 Γ— origin Β± 1)
2^2 Γ— origin βˆ’ 1
4.137 Γ— 10⁹⁸(99-digit number)
41370465958171173933…39433710307914927359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.137 Γ— 10⁹⁸(99-digit number)
41370465958171173933…39433710307914927361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^2 Γ— origin + 1 βˆ’ 2^2 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 3 β€” Twin Prime Pair (2^3 Γ— origin Β± 1)
2^3 Γ— origin βˆ’ 1
8.274 Γ— 10⁹⁸(99-digit number)
82740931916342347867…78867420615829854719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
8.274 Γ— 10⁹⁸(99-digit number)
82740931916342347867…78867420615829854721
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^3 Γ— origin + 1 βˆ’ 2^3 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 4 β€” Twin Prime Pair (2^4 Γ— origin Β± 1)
2^4 Γ— origin βˆ’ 1
1.654 Γ— 10⁹⁹(100-digit number)
16548186383268469573…57734841231659709439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.654 Γ— 10⁹⁹(100-digit number)
16548186383268469573…57734841231659709441
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)

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 β€” the large number shown above β€” anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

β˜…β˜…β˜†β˜†β˜†
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 Γ— 3 Γ— 5 Γ— 7 Γ— …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial β€” that divisibility is part of the proof.

Prime Chain Origin = First Prime Γ— Primorial (2Β·3Β·5Β·7Β·11·…)
Source: Primecoin prime.cpp β€” CheckPrimeProofOfWork()

This is why the origin has many small prime factors β€” 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 βˆ’ 1 and p+2 = origin/primorial + 1
Cross-reference on Chainz Explorer
Circulating Supply:57,840,536 XPMΒ·at block #6,824,558 Β· updates every 60s
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