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Block #667,705

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/7/2014, 7:22:07 PM Β· Difficulty 10.9629 Β· 6,141,707 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
f1c888a61babdc5fa517436c3cee65d71d0b61b54b581092dc86a9c8f4645577
View on Chainz β†—

Height

#667,705

Difficulty

10.962927

Transactions

2

Size

1.00 KB

Version

2

Bits

0af6825b

Nonce

186,084,130

Timestamp

8/7/2014, 7:22:07 PM

Confirmations

6,141,707

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

9907ce9d57ab749df28d4236e072f50c69fb0a78c934f7b41aad37b40bc39ff3
Transactions (2)
Coinbased16d71b78065c4…d9d4f7a1f2a847
1 in β†’ 1 out8.3200 XPM116 B
ANSXnLY2…Sd25TjkD
dafc67083c8951…39a097a1c6de8f
5 in β†’ 2 out4.0320 XPM817 B
AM464ysq…J3E3XKMoAdLFT1xa…tw8SAGdm
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.

1.491 Γ— 10⁹⁷(98-digit number)
14915199233456345040…14672419975947801599
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
1.491 Γ— 10⁹⁷(98-digit number)
14915199233456345040…14672419975947801599
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.491 Γ— 10⁹⁷(98-digit number)
14915199233456345040…14672419975947801601
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
2.983 Γ— 10⁹⁷(98-digit number)
29830398466912690080…29344839951895603199
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
2.983 Γ— 10⁹⁷(98-digit number)
29830398466912690080…29344839951895603201
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
5.966 Γ— 10⁹⁷(98-digit number)
59660796933825380161…58689679903791206399
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
5.966 Γ— 10⁹⁷(98-digit number)
59660796933825380161…58689679903791206401
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
1.193 Γ— 10⁹⁸(99-digit number)
11932159386765076032…17379359807582412799
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.193 Γ— 10⁹⁸(99-digit number)
11932159386765076032…17379359807582412801
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
2.386 Γ— 10⁹⁸(99-digit number)
23864318773530152064…34758719615164825599
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.386 Γ— 10⁹⁸(99-digit number)
23864318773530152064…34758719615164825601
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:57,719,371 XPMΒ·at block #6,809,411 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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