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Block #1,749,390

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/5/2016, 7:03:16 PM Β· Difficulty 10.6972 Β· 5,076,046 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
dc8c6348e8bfddd4c6f9826c3596c9da288c51480564376b33759e22effee580
View on Chainz β†—

Height

#1,749,390

Difficulty

10.697227

Transactions

2

Size

575 B

Version

2

Bits

0ab27d76

Nonce

603,079,601

Timestamp

9/5/2016, 7:03:16 PM

Confirmations

5,076,046

Mined by

⛏️ P2SHAf6Hzy2Rx8DAL3Arg6MMw49q91UkEpV5tg

Merkle Root

68a8f204488843bed275c8b91c11ccdcbc13fc543c8b135a4eb8b883a85f9fca
Transactions (2)
Coinbase16decf2bf8bd75…0f76d549c6e38d
1 in β†’ 1 out8.7400 XPM110 B
Af6Hzy2R…UkEpV5tg
f7de9fcc2a6fae…30e8d4e2ee48dd
2 in β†’ 2 out4.1613 XPM375 B
AU1BRopg…h8vsNHDaALCyLDdk…9jK3XeGp
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.

2.134 Γ— 10⁹⁴(95-digit number)
21341159594943657738…36445142688114776079
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
2.134 Γ— 10⁹⁴(95-digit number)
21341159594943657738…36445142688114776079
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.134 Γ— 10⁹⁴(95-digit number)
21341159594943657738…36445142688114776081
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
4.268 Γ— 10⁹⁴(95-digit number)
42682319189887315476…72890285376229552159
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
4.268 Γ— 10⁹⁴(95-digit number)
42682319189887315476…72890285376229552161
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
8.536 Γ— 10⁹⁴(95-digit number)
85364638379774630952…45780570752459104319
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
8.536 Γ— 10⁹⁴(95-digit number)
85364638379774630952…45780570752459104321
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
1.707 Γ— 10⁹⁡(96-digit number)
17072927675954926190…91561141504918208639
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.707 Γ— 10⁹⁡(96-digit number)
17072927675954926190…91561141504918208641
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
3.414 Γ— 10⁹⁡(96-digit number)
34145855351909852381…83122283009836417279
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.414 Γ— 10⁹⁡(96-digit number)
34145855351909852381…83122283009836417281
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:57,847,591 XPMΒ·at block #6,825,435 Β· updates every 60s
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