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Block #1,453,970

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/13/2016, 4:24:30 AM Β· Difficulty 10.7241 Β· 5,388,778 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7dc2908122aaae97ad027e89b37fa8e34ded7534926852e76fe6435ab495771e
View on Chainz β†—

Height

#1,453,970

Difficulty

10.724132

Transactions

1

Size

200 B

Version

2

Bits

0ab960bd

Nonce

998,156,609

Timestamp

2/13/2016, 4:24:30 AM

Confirmations

5,388,778

Mined by

⛏️ P2SHAHoFsspRNhXQY8z2764zGH5JnMrZmueFSf

Merkle Root

6dc037a97c4d59c06e1f3c0f1a188bdd6467275062dcd1530d15b61b82948254
Transactions (1)
Coinbase6dc037a97c4d59…15b61b82948254
1 in β†’ 1 out8.6800 XPM110 B
AHoFsspR…rZmueFSf
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.

1.177 Γ— 10⁹⁡(96-digit number)
11773935497810838614…43224780022929293439
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
1.177 Γ— 10⁹⁡(96-digit number)
11773935497810838614…43224780022929293439
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.177 Γ— 10⁹⁡(96-digit number)
11773935497810838614…43224780022929293441
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
2.354 Γ— 10⁹⁡(96-digit number)
23547870995621677229…86449560045858586879
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.354 Γ— 10⁹⁡(96-digit number)
23547870995621677229…86449560045858586881
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
4.709 Γ— 10⁹⁡(96-digit number)
47095741991243354458…72899120091717173759
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
4.709 Γ— 10⁹⁡(96-digit number)
47095741991243354458…72899120091717173761
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
9.419 Γ— 10⁹⁡(96-digit number)
94191483982486708916…45798240183434347519
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
9.419 Γ— 10⁹⁡(96-digit number)
94191483982486708916…45798240183434347521
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
1.883 Γ— 10⁹⁢(97-digit number)
18838296796497341783…91596480366868695039
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.883 Γ— 10⁹⁢(97-digit number)
18838296796497341783…91596480366868695041
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:57,986,321 XPMΒ·at block #6,842,747 Β· updates every 60s
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