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Block #929,247

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/9/2015, 4:16:35 PM Β· Difficulty 10.9037 Β· 5,876,975 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
8d53fc85b63148ceba02c6ec0d81c3687b57fa94ae4a88547d87578045825b6d
View on Chainz β†—

Height

#929,247

Difficulty

10.903653

Transactions

2

Size

365 B

Version

2

Bits

0ae755c6

Nonce

15,655,017

Timestamp

2/9/2015, 4:16:35 PM

Confirmations

5,876,975

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f6b597fe4ccad0992526ca1c325834d4555ce82394fef2b4e7fa9562abcae5ae
Transactions (2)
Coinbase233dfae86216f4…e1748aa70d686e
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
d5ed80ba65f6e3…c538500bf109c5
1 in β†’ 1 out8.3800 XPM158 B
AekLq4Sw…ueWMfyir
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.

8.154 Γ— 10⁹⁢(97-digit number)
81545423465329584000…16312631587606655999
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
8.154 Γ— 10⁹⁢(97-digit number)
81545423465329584000…16312631587606655999
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
8.154 Γ— 10⁹⁢(97-digit number)
81545423465329584000…16312631587606656001
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
1.630 Γ— 10⁹⁷(98-digit number)
16309084693065916800…32625263175213311999
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.630 Γ— 10⁹⁷(98-digit number)
16309084693065916800…32625263175213312001
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
3.261 Γ— 10⁹⁷(98-digit number)
32618169386131833600…65250526350426623999
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
3.261 Γ— 10⁹⁷(98-digit number)
32618169386131833600…65250526350426624001
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
6.523 Γ— 10⁹⁷(98-digit number)
65236338772263667200…30501052700853247999
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
6.523 Γ— 10⁹⁷(98-digit number)
65236338772263667200…30501052700853248001
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
1.304 Γ— 10⁹⁸(99-digit number)
13047267754452733440…61002105401706495999
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
1.304 Γ— 10⁹⁸(99-digit number)
13047267754452733440…61002105401706496001
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:57,693,856 XPMΒ·at block #6,806,221 Β· updates every 60s
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