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Block #580,938

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 6/8/2014, 6:43:22 AM Β· Difficulty 10.9637 Β· 6,245,244 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
e25ee7093d9559841a8eb016f3421997b9666e7c905c649fe937f446ae16fb7b
View on Chainz β†—

Height

#580,938

Difficulty

10.963654

Transactions

2

Size

433 B

Version

2

Bits

0af6b206

Nonce

1,451,617,974

Timestamp

6/8/2014, 6:43:22 AM

Confirmations

6,245,244

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

4a4302db5f3f2949693f944f31f11e2b3b7e05a3fee5b8772dca0bb1b0a0bace
Transactions (2)
Coinbase5f261f3fbf4aa5…95fda95282fe80
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
a45a279c0fe091…fae0c331700517
1 in β†’ 2 out7056.0369 XPM226 B
AXMfmMk1…5RcM2TkqAPRWSjBU…A24rJqGA
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.

9.808 Γ— 10⁹⁷(98-digit number)
98080871380239132848…30603427085559609119
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
9.808 Γ— 10⁹⁷(98-digit number)
98080871380239132848…30603427085559609119
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
9.808 Γ— 10⁹⁷(98-digit number)
98080871380239132848…30603427085559609121
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
1.961 Γ— 10⁹⁸(99-digit number)
19616174276047826569…61206854171119218239
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.961 Γ— 10⁹⁸(99-digit number)
19616174276047826569…61206854171119218241
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
3.923 Γ— 10⁹⁸(99-digit number)
39232348552095653139…22413708342238436479
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.923 Γ— 10⁹⁸(99-digit number)
39232348552095653139…22413708342238436481
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
7.846 Γ— 10⁹⁸(99-digit number)
78464697104191306279…44827416684476872959
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
7.846 Γ— 10⁹⁸(99-digit number)
78464697104191306279…44827416684476872961
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
1.569 Γ— 10⁹⁹(100-digit number)
15692939420838261255…89654833368953745919
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.569 Γ— 10⁹⁹(100-digit number)
15692939420838261255…89654833368953745921
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:57,853,585 XPMΒ·at block #6,826,181 Β· updates every 60s
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