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Block #1,407,223

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 1/10/2016, 11:01:49 AM Β· Difficulty 10.8061 Β· 5,435,204 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
af866b642cf4e0711e3b3b89e0389a7f77173df676756eb92fda630b5e4f038e
View on Chainz β†—

Height

#1,407,223

Difficulty

10.806135

Transactions

2

Size

426 B

Version

2

Bits

0ace5ee0

Nonce

101,588,328

Timestamp

1/10/2016, 11:01:49 AM

Confirmations

5,435,204

Mined by

⛏️ P2SHAP2G2WC67e1eB8Hzk6MdUqgpFiBHUn3sx6

Merkle Root

a389c4f9f845a27b47a723f4338ec5a2f115cdd1a9fdde4d974f31b2186c5545
Transactions (2)
Coinbasebc1c75fe022467…749846c20d2bb1
1 in β†’ 1 out8.5600 XPM110 B
AP2G2WC6…BHUn3sx6
a067474b6bd27d…88163fb3bb97cb
1 in β†’ 2 out147988.4337 XPM226 B
AeGqejXF…u3fJjJReAQz5cxT1…6bpmEdXY
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.

1.324 Γ— 10⁹⁴(95-digit number)
13246874656667479731…97795289895182234479
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
1.324 Γ— 10⁹⁴(95-digit number)
13246874656667479731…97795289895182234479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.324 Γ— 10⁹⁴(95-digit number)
13246874656667479731…97795289895182234481
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
2.649 Γ— 10⁹⁴(95-digit number)
26493749313334959462…95590579790364468959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.649 Γ— 10⁹⁴(95-digit number)
26493749313334959462…95590579790364468961
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
5.298 Γ— 10⁹⁴(95-digit number)
52987498626669918925…91181159580728937919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.298 Γ— 10⁹⁴(95-digit number)
52987498626669918925…91181159580728937921
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
1.059 Γ— 10⁹⁡(96-digit number)
10597499725333983785…82362319161457875839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.059 Γ— 10⁹⁡(96-digit number)
10597499725333983785…82362319161457875841
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
2.119 Γ— 10⁹⁡(96-digit number)
21194999450667967570…64724638322915751679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.119 Γ— 10⁹⁡(96-digit number)
21194999450667967570…64724638322915751681
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:57,983,830 XPMΒ·at block #6,842,426 Β· updates every 60s
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