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Block #818,592

TWNLength 11β˜…β˜…β˜…β˜†β˜†

Bi-Twin Chain Β· Discovered 11/19/2014, 2:29:48 PM Β· Difficulty 10.9763 Β· 5,979,361 confirmations

TWN
Bi-Twin Chain

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

Block Header
Block Hash
3660f0de44c53bd9850d999d3107ecd9f7f38996b553e539bf7f7207761a0e3d
View on Chainz β†—

Height

#818,592

Difficulty

10.976265

Transactions

2

Size

878 B

Version

2

Bits

0af9ec87

Nonce

145,467,212

Timestamp

11/19/2014, 2:29:48 PM

Confirmations

5,979,361

Mined by

⛏️ P2SHANSXnLY2HX2a5e6fdcDUZDtfwTSd25TjkD

Merkle Root

f268086daec2ec821b5ed80376527c71f2190bd4d7e95ec12275a22b984e0262
Transactions (2)
Coinbasec18431b0eb6996…d94029e86db4ed
1 in β†’ 1 out8.3000 XPM116 B
ANSXnLY2…Sd25TjkD
224c3085a4e593…215818a0b4ad32
4 in β†’ 2 out215.0408 XPM671 B
AMDozip1…gVp8Ptz5AX5cVzvj…1Nof9SQm
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.

4.634 Γ— 10⁹⁢(97-digit number)
46346409194084208771…29519616530671967359
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
4.634 Γ— 10⁹⁢(97-digit number)
46346409194084208771…29519616530671967359
Verify on FactorDB β†—Wolfram Alpha β†—
origin + 1
4.634 Γ— 10⁹⁢(97-digit number)
46346409194084208771…29519616530671967361
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
9.269 Γ— 10⁹⁢(97-digit number)
92692818388168417543…59039233061343934719
Verify on FactorDB β†—Wolfram Alpha β†—
2^1 Γ— origin + 1
9.269 Γ— 10⁹⁢(97-digit number)
92692818388168417543…59039233061343934721
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
1.853 Γ— 10⁹⁷(98-digit number)
18538563677633683508…18078466122687869439
Verify on FactorDB β†—Wolfram Alpha β†—
2^2 Γ— origin + 1
1.853 Γ— 10⁹⁷(98-digit number)
18538563677633683508…18078466122687869441
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
3.707 Γ— 10⁹⁷(98-digit number)
37077127355267367017…36156932245375738879
Verify on FactorDB β†—Wolfram Alpha β†—
2^3 Γ— origin + 1
3.707 Γ— 10⁹⁷(98-digit number)
37077127355267367017…36156932245375738881
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
7.415 Γ— 10⁹⁷(98-digit number)
74154254710534734034…72313864490751477759
Verify on FactorDB β†—Wolfram Alpha β†—
2^4 Γ— origin + 1
7.415 Γ— 10⁹⁷(98-digit number)
74154254710534734034…72313864490751477761
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
1.483 Γ— 10⁹⁸(99-digit number)
14830850942106946806…44627728981502955519
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:57,627,617 XPMΒ·at block #6,797,952 Β· updates every 60s
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