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Block #1,371,704

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 12/16/2015, 4:26:21 PM Β· Difficulty 10.8109 Β· 5,469,690 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
36c395a925a41f346811cd5b55d8fc8a9bf443cf66c5bee1c4c789f5c3bfd039
View on Chainz β†—

Height

#1,371,704

Difficulty

10.810908

Transactions

2

Size

541 B

Version

2

Bits

0acf97af

Nonce

887,349,233

Timestamp

12/16/2015, 4:26:21 PM

Confirmations

5,469,690

Mined by

⛏️ P2SHAeoBaAucfieZJHNdTGrsLBHvUXtsmEr3hh

Merkle Root

be935ef26b0c0b37b55013adbf759dabb666e8b2d22cbe41dd4c0beb5f1b7345
Transactions (2)
Coinbase2c1ebf777af7d5…3f71d8a3fef315
1 in β†’ 1 out8.5500 XPM110 B
AeoBaAuc…tsmEr3hh
e57d6499272573…63dfcf110e09d5
2 in β†’ 1 out13.9900 XPM340 B
AQPFnLD1…m4GCG1nH
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.

7.608 Γ— 10⁹⁢(97-digit number)
76083376643262858225…42073096454007504639
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
7.608 Γ— 10⁹⁢(97-digit number)
76083376643262858225…42073096454007504639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
7.608 Γ— 10⁹⁢(97-digit number)
76083376643262858225…42073096454007504641
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
1.521 Γ— 10⁹⁷(98-digit number)
15216675328652571645…84146192908015009279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.521 Γ— 10⁹⁷(98-digit number)
15216675328652571645…84146192908015009281
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
3.043 Γ— 10⁹⁷(98-digit number)
30433350657305143290…68292385816030018559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.043 Γ— 10⁹⁷(98-digit number)
30433350657305143290…68292385816030018561
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
6.086 Γ— 10⁹⁷(98-digit number)
60866701314610286580…36584771632060037119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.086 Γ— 10⁹⁷(98-digit number)
60866701314610286580…36584771632060037121
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
1.217 Γ— 10⁹⁸(99-digit number)
12173340262922057316…73169543264120074239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.217 Γ— 10⁹⁸(99-digit number)
12173340262922057316…73169543264120074241
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:57,975,524 XPMΒ·at block #6,841,393 Β· updates every 60s
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