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Block #2,925,096

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 7:16:59 AM Β· Difficulty 11.3547 Β· 3,916,734 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
7cb5fd420c7f5675d838609b0477a2b5e7445836e739fa0951905b5bea22101d
View on Chainz β†—

Height

#2,925,096

Difficulty

11.354720

Transactions

1

Size

200 B

Version

2

Bits

0b5acee9

Nonce

1,646,930,774

Timestamp

11/16/2018, 7:16:59 AM

Confirmations

3,916,734

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

4f0fa845a44128137730eb664794bfd41bb85e4b05ca72b6c834d276293a6ddd
Transactions (1)
Coinbase4f0fa845a44128…34d276293a6ddd
1 in β†’ 1 out7.7400 XPM109 B
AbXwmGxD…4XXYP765
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.

1.651 Γ— 10⁹⁢(97-digit number)
16513216416809238996…73475430316645416959
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
1.651 Γ— 10⁹⁢(97-digit number)
16513216416809238996…73475430316645416959
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.651 Γ— 10⁹⁢(97-digit number)
16513216416809238996…73475430316645416961
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
3.302 Γ— 10⁹⁢(97-digit number)
33026432833618477993…46950860633290833919
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.302 Γ— 10⁹⁢(97-digit number)
33026432833618477993…46950860633290833921
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
6.605 Γ— 10⁹⁢(97-digit number)
66052865667236955986…93901721266581667839
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
6.605 Γ— 10⁹⁢(97-digit number)
66052865667236955986…93901721266581667841
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
1.321 Γ— 10⁹⁷(98-digit number)
13210573133447391197…87803442533163335679
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.321 Γ— 10⁹⁷(98-digit number)
13210573133447391197…87803442533163335681
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
2.642 Γ— 10⁹⁷(98-digit number)
26421146266894782394…75606885066326671359
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
2.642 Γ— 10⁹⁷(98-digit number)
26421146266894782394…75606885066326671361
Verify on FactorDB β†—Wolfram Alpha β†—
Difference: 2^4 Γ— origin + 1 βˆ’ 2^4 Γ— origin βˆ’ 1 = 2 (twin primes βœ“)
Level 5 β€” Twin Prime Pair (2^5 Γ— origin Β± 1)
2^5 Γ— origin βˆ’ 1
5.284 Γ— 10⁹⁷(98-digit number)
52842292533789564789…51213770132653342719
Verify on FactorDB β†—Wolfram Alpha β†—

What this block proved

The miner who found this block proved the existence of 11 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
RareChain length 11

Approximately 1 in 1,000 blocks. Noteworthy discoveries.

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:57,979,013 XPMΒ·at block #6,841,829 Β· updates every 60s
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