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Block #2,652,009

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 5/7/2018, 6:40:48 AM Β· Difficulty 11.7475 Β· 4,189,478 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
123b5f80d5bde20e069eab02cbc26c5d415628ed43c918ae1ce6f0f253de05a1
View on Chainz β†—

Height

#2,652,009

Difficulty

11.747483

Transactions

2

Size

426 B

Version

2

Bits

0bbf5b0c

Nonce

2,035,514,127

Timestamp

5/7/2018, 6:40:48 AM

Confirmations

4,189,478

Mined by

⛏️ P2SHAGx1Vb8QnEXmvviBuc1BUVWGZ4jM967jqF

Merkle Root

72fa198484d87efe48482005e542d47d1c5191944e457323b89ef81c6a73e60a
Transactions (2)
Coinbasecec7fbd34adcad…10e05d213ba348
1 in β†’ 1 out7.2400 XPM110 B
AGx1Vb8Q…jM967jqF
b203f21937fd36…53a2fd788c9d53
1 in β†’ 2 out3.8900 XPM225 B
AcBFggS9…BKG7ekrEAPSdSs6C…Ukaxq6S9
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.

4.800 Γ— 10⁹⁢(97-digit number)
48001411686745101645…30816762341006938879
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
4.800 Γ— 10⁹⁢(97-digit number)
48001411686745101645…30816762341006938879
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.800 Γ— 10⁹⁢(97-digit number)
48001411686745101645…30816762341006938881
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
9.600 Γ— 10⁹⁢(97-digit number)
96002823373490203291…61633524682013877759
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.600 Γ— 10⁹⁢(97-digit number)
96002823373490203291…61633524682013877761
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
1.920 Γ— 10⁹⁷(98-digit number)
19200564674698040658…23267049364027755519
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.920 Γ— 10⁹⁷(98-digit number)
19200564674698040658…23267049364027755521
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
3.840 Γ— 10⁹⁷(98-digit number)
38401129349396081316…46534098728055511039
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.840 Γ— 10⁹⁷(98-digit number)
38401129349396081316…46534098728055511041
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
7.680 Γ— 10⁹⁷(98-digit number)
76802258698792162633…93068197456111022079
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.680 Γ— 10⁹⁷(98-digit number)
76802258698792162633…93068197456111022081
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
1.536 Γ— 10⁹⁸(99-digit number)
15360451739758432526…86136394912222044159
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:57,976,272 XPMΒ·at block #6,841,486 Β· updates every 60s
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