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Block #792,311

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 11/1/2014, 2:58:24 PM Β· Difficulty 10.9735 Β· 6,007,192 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
a337c142a78ae7e7cede702a9a66dff76ecd16764b5368dacdd83121a1682606
View on Chainz β†—

Height

#792,311

Difficulty

10.973508

Transactions

3

Size

659 B

Version

2

Bits

0af937cc

Nonce

231,314,018

Timestamp

11/1/2014, 2:58:24 PM

Confirmations

6,007,192

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

30a406382b9b51842f4217de50be30aa0c4ecd950c7b3ec414ec593672e68e68
Transactions (3)
Coinbasec13f6ff35a14e7…0855f0abd47159
1 in β†’ 1 out8.3100 XPM116 B
ANSXnLY2…Sd25TjkD
88ebfbf4073534…58a8869eb39b32
1 in β†’ 2 out8.2700 XPM227 B
AREmLC5L…3hsWg33iAUv8Sqca…fd6ms9WK
7278519d36cf56…3806e5a4490e5f
1 in β†’ 2 out8.2700 XPM226 B
AV4ANiYC…Nhv7LxVJAGEed55R…9o5EJWws
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.

1.645 Γ— 10⁹⁡(96-digit number)
16451183288529579796…14131967659666828679
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
1.645 Γ— 10⁹⁡(96-digit number)
16451183288529579796…14131967659666828679
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.645 Γ— 10⁹⁡(96-digit number)
16451183288529579796…14131967659666828681
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
3.290 Γ— 10⁹⁡(96-digit number)
32902366577059159593…28263935319333657359
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.290 Γ— 10⁹⁡(96-digit number)
32902366577059159593…28263935319333657361
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
6.580 Γ— 10⁹⁡(96-digit number)
65804733154118319186…56527870638667314719
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.580 Γ— 10⁹⁡(96-digit number)
65804733154118319186…56527870638667314721
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
1.316 Γ— 10⁹⁢(97-digit number)
13160946630823663837…13055741277334629439
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.316 Γ— 10⁹⁢(97-digit number)
13160946630823663837…13055741277334629441
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
2.632 Γ— 10⁹⁢(97-digit number)
26321893261647327674…26111482554669258879
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.632 Γ— 10⁹⁢(97-digit number)
26321893261647327674…26111482554669258881
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:57,640,070 XPMΒ·at block #6,799,502 Β· updates every 60s
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