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Block #1,715,459

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/13/2016, 3:29:20 PM Β· Difficulty 10.6576 Β· 5,115,554 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f8d9744aba352a99e02f0004a66c165ee99beec151ba21db662c4b51d2daabe0
View on Chainz β†—

Height

#1,715,459

Difficulty

10.657630

Transactions

1

Size

243 B

Version

2

Bits

0aa85a72

Nonce

131,988,524

Timestamp

8/13/2016, 3:29:20 PM

Confirmations

5,115,554

Mined by

⛏️ P2SHAMeY5ZrV7AqtjFwPLjnwr3BDd53veG96Ko

Merkle Root

8e18350a950b54889f731dda2c39eb3cebaeb84ec9ab91fc9d746a6be53fb992
Transactions (1)
Coinbase8e18350a950b54…746a6be53fb992
1 in β†’ 2 out8.7900 XPM152 B
AMeY5ZrV…3veG96KoALPu3s2c…EJXLjVFh
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.

2.460 Γ— 10⁹⁢(97-digit number)
24603000163235887434…78947803788078194559
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
2.460 Γ— 10⁹⁢(97-digit number)
24603000163235887434…78947803788078194559
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.460 Γ— 10⁹⁢(97-digit number)
24603000163235887434…78947803788078194561
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
4.920 Γ— 10⁹⁢(97-digit number)
49206000326471774869…57895607576156389119
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.920 Γ— 10⁹⁢(97-digit number)
49206000326471774869…57895607576156389121
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
9.841 Γ— 10⁹⁢(97-digit number)
98412000652943549739…15791215152312778239
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
9.841 Γ— 10⁹⁢(97-digit number)
98412000652943549739…15791215152312778241
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
1.968 Γ— 10⁹⁷(98-digit number)
19682400130588709947…31582430304625556479
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.968 Γ— 10⁹⁷(98-digit number)
19682400130588709947…31582430304625556481
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
3.936 Γ— 10⁹⁷(98-digit number)
39364800261177419895…63164860609251112959
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.936 Γ— 10⁹⁷(98-digit number)
39364800261177419895…63164860609251112961
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:57,892,245 XPMΒ·at block #6,831,012 Β· updates every 60s
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