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Block #2,925,016

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/16/2018, 5:45:07 AM Β· Difficulty 11.3562 Β· 3,916,649 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
b99a884b0f953a52fed76efa5f45c1026eeb648cda2f24f2152ce1f11c836946
View on Chainz β†—

Height

#2,925,016

Difficulty

11.356246

Transactions

1

Size

201 B

Version

2

Bits

0b5b32f8

Nonce

1,123,052,065

Timestamp

11/16/2018, 5:45:07 AM

Confirmations

3,916,649

Mined by

⛏️ P2SHAbXwmGxDc5ZxwPwgT1QckjRUmF4XXYP765

Merkle Root

098944d9f32a66a9718c5ef1f3d2eb317e0edd43b785b229764c848e4dd718df
Transactions (1)
Coinbase098944d9f32a66…4c848e4dd718df
1 in β†’ 1 out7.7400 XPM110 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.

1.930 Γ— 10⁹⁢(97-digit number)
19304637069723827405…93835268939175408639
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
1.930 Γ— 10⁹⁢(97-digit number)
19304637069723827405…93835268939175408639
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
1.930 Γ— 10⁹⁢(97-digit number)
19304637069723827405…93835268939175408641
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
3.860 Γ— 10⁹⁢(97-digit number)
38609274139447654810…87670537878350817279
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
3.860 Γ— 10⁹⁢(97-digit number)
38609274139447654810…87670537878350817281
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
7.721 Γ— 10⁹⁢(97-digit number)
77218548278895309620…75341075756701634559
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
7.721 Γ— 10⁹⁢(97-digit number)
77218548278895309620…75341075756701634561
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
1.544 Γ— 10⁹⁷(98-digit number)
15443709655779061924…50682151513403269119
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
1.544 Γ— 10⁹⁷(98-digit number)
15443709655779061924…50682151513403269121
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
3.088 Γ— 10⁹⁷(98-digit number)
30887419311558123848…01364303026806538239
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
3.088 Γ— 10⁹⁷(98-digit number)
30887419311558123848…01364303026806538241
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
6.177 Γ— 10⁹⁷(98-digit number)
61774838623116247696…02728606053613076479
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:57,977,709 XPMΒ·at block #6,841,664 Β· updates every 60s
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