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Block #1,729,088

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 8/22/2016, 12:26:43 PM Β· Difficulty 10.7114 Β· 5,098,048 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
17a3336aee7f2a9fdda1271e3389f9012f658120d1d8b2f013d6b6c1cac64d5d
View on Chainz β†—

Height

#1,729,088

Difficulty

10.711362

Transactions

1

Size

200 B

Version

2

Bits

0ab61bd0

Nonce

597,576,725

Timestamp

8/22/2016, 12:26:43 PM

Confirmations

5,098,048

Mined by

⛏️ P2SHARjSVHwTN63ntLvNh4YFWQ6r7BRkoXGeyt

Merkle Root

8a85c67c5123c7a447e02bca62fe2423aaf996c7564de8f3e4ba92ce6edbb165
Transactions (1)
Coinbase8a85c67c5123c7…ba92ce6edbb165
1 in β†’ 1 out8.7000 XPM109 B
ARjSVHwT…RkoXGeyt
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.

4.834 Γ— 10⁹⁢(97-digit number)
48343204739610580641…49218485294992916479
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
4.834 Γ— 10⁹⁢(97-digit number)
48343204739610580641…49218485294992916479
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.834 Γ— 10⁹⁢(97-digit number)
48343204739610580641…49218485294992916481
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
9.668 Γ— 10⁹⁢(97-digit number)
96686409479221161282…98436970589985832959
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.668 Γ— 10⁹⁢(97-digit number)
96686409479221161282…98436970589985832961
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
1.933 Γ— 10⁹⁷(98-digit number)
19337281895844232256…96873941179971665919
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.933 Γ— 10⁹⁷(98-digit number)
19337281895844232256…96873941179971665921
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
3.867 Γ— 10⁹⁷(98-digit number)
38674563791688464513…93747882359943331839
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.867 Γ— 10⁹⁷(98-digit number)
38674563791688464513…93747882359943331841
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
7.734 Γ— 10⁹⁷(98-digit number)
77349127583376929026…87495764719886663679
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.734 Γ— 10⁹⁷(98-digit number)
77349127583376929026…87495764719886663681
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:57,861,269 XPMΒ·at block #6,827,135 Β· updates every 60s
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