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Block #928,704

TWNLength 10β˜…β˜…β˜†β˜†β˜†

Bi-Twin Chain Β· Discovered 2/9/2015, 7:15:13 AM Β· Difficulty 10.9036 Β· 5,881,716 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
716c4e9bd10aa27d6b66cde78650801736d0dbfff3680becac6d95d26242d3fb
View on Chainz β†—

Height

#928,704

Difficulty

10.903599

Transactions

2

Size

364 B

Version

2

Bits

0ae75241

Nonce

267,441,944

Timestamp

2/9/2015, 7:15:13 AM

Confirmations

5,881,716

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

2cb2308e72cf34a7cca3ae2c89a3c041737af9c03b7dc63ec1eebb7bf763e61b
Transactions (2)
Coinbasee3c9efb26daf18…81e87a46232c3e
1 in β†’ 1 out8.4100 XPM116 B
ANSXnLY2…Sd25TjkD
d92691c6029ca9…ec1bf2af460513
1 in β†’ 1 out8.3800 XPM157 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.

6.021 Γ— 10⁹⁢(97-digit number)
60219343589119119883…53512089652459806719
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
6.021 Γ— 10⁹⁢(97-digit number)
60219343589119119883…53512089652459806719
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
6.021 Γ— 10⁹⁢(97-digit number)
60219343589119119883…53512089652459806721
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
1.204 Γ— 10⁹⁷(98-digit number)
12043868717823823976…07024179304919613439
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
1.204 Γ— 10⁹⁷(98-digit number)
12043868717823823976…07024179304919613441
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
2.408 Γ— 10⁹⁷(98-digit number)
24087737435647647953…14048358609839226879
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
2.408 Γ— 10⁹⁷(98-digit number)
24087737435647647953…14048358609839226881
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
4.817 Γ— 10⁹⁷(98-digit number)
48175474871295295906…28096717219678453759
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
4.817 Γ— 10⁹⁷(98-digit number)
48175474871295295906…28096717219678453761
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
9.635 Γ— 10⁹⁷(98-digit number)
96350949742590591813…56193434439356907519
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
9.635 Γ— 10⁹⁷(98-digit number)
96350949742590591813…56193434439356907521
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:57,727,441 XPMΒ·at block #6,810,419 Β· updates every 60s
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AQZeJoQ81VgeHQBpEYTgvNqV1gnz3L5SvK

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