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Block #726,138

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 9/17/2014, 5:43:08 PM Β· Difficulty 10.9608 Β· 6,083,396 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
1b92abfc1c91569208769bab3c766ecf70af9d68c37a0722f9dfea9e6f3c16a8
View on Chainz β†—

Height

#726,138

Difficulty

10.960797

Transactions

2

Size

1.58 KB

Version

2

Bits

0af5f6cd

Nonce

56,553,221

Timestamp

9/17/2014, 5:43:08 PM

Confirmations

6,083,396

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

60636493e01d3d6b69f261c7f34aaa7a65b4528b799e40021f71ad93d965e655
Transactions (2)
Coinbaseb190b0b9d198ee…3e7b3361d866cc
1 in β†’ 1 out8.3300 XPM116 B
ANSXnLY2…Sd25TjkD
58fc013820f253…9d337a1f184472
9 in β†’ 2 out710.3171 XPM1.38 KB
Abjzhj6c…9JKBk3RiAHxVvCiZ…x8sUznk2
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.

2.647 Γ— 10⁹⁷(98-digit number)
26473157074676853207…51473912552055619839
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
2.647 Γ— 10⁹⁷(98-digit number)
26473157074676853207…51473912552055619839
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
2.647 Γ— 10⁹⁷(98-digit number)
26473157074676853207…51473912552055619841
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
5.294 Γ— 10⁹⁷(98-digit number)
52946314149353706415…02947825104111239679
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
5.294 Γ— 10⁹⁷(98-digit number)
52946314149353706415…02947825104111239681
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
1.058 Γ— 10⁹⁸(99-digit number)
10589262829870741283…05895650208222479359
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.058 Γ— 10⁹⁸(99-digit number)
10589262829870741283…05895650208222479361
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
2.117 Γ— 10⁹⁸(99-digit number)
21178525659741482566…11791300416444958719
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
2.117 Γ— 10⁹⁸(99-digit number)
21178525659741482566…11791300416444958721
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
4.235 Γ— 10⁹⁸(99-digit number)
42357051319482965132…23582600832889917439
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
4.235 Γ— 10⁹⁸(99-digit number)
42357051319482965132…23582600832889917441
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:57,720,351 XPMΒ·at block #6,809,533 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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